A committee

A committee of 6 is chosen from 8 men and seven women. Find how many committees are possible if a particular man must be included.

Correct answer:

n =  4998

Step-by-step explanation:

C1(8)=(18)=1!(81)!8!=18=8  C5(7)=(57)=5!(75)!7!=2176=21  C3(8)=(38)=3!(83)!8!=321876=56  C5(8)=(58)=5!(85)!8!=321876=56  a=(18) (57)=8 21=168 C2(8)=(28)=2!(82)!8!=2187=28  C4(7)=(47)=4!(74)!7!=321765=35  C4(8)=(48)=4!(84)!8!=43218765=70  b=(28) (47)=28 35=980 C3(7)=(37)=3!(73)!7!=321765=35  c=(38) (37)=56 35=1960 C2(7)=(27)=2!(72)!7!=2176=21  d=(48) (27)=70 21=1470 C1(7)=(17)=1!(71)!7!=17=7  e=(58) (17)=56 7=392 C6(8)=(68)=6!(86)!8!=2187=28  C0(7)=(07)=0!(70)!7!=11=1  f=(68) (07)=28 1=28  n=a+b+c+d+e+f=168+980+1960+1470+392+28=4998

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Showing 1 comment:
Math student
The answer is actually 14C5=2002

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